The models of Cormack, Jolly and Seber (CJS) are remarkable in providing a rich set of inferences about population survival, recruitment, abundance and even sampling probabilities from a seemingly limited data source: a matrix of 1’s and 0’s reflecting animal captures and recaptures at multiple sampling occasions. Survival and sampling probabilities are estimated directly in CJS models, whereas estimators for recruitment and abundance were initially obtained as derived quantities. Various investigators have noted that just as standard modeling provides direct inferences about survival, reversing the time order of capture history data permits direct modeling and inference about recruitment. Here we review the development of reverse-time modeling efforts, emphasizing the kinds of inferences and questions to which they seem well suited.
"And the First One Now Will Later Be Last: Time-Reversal in Cormack–Jolly–Seber Models." Statist. Sci. 31 (2) 175 - 190, May 2016. https://doi.org/10.1214/16-STS546